tsani's Interpretations: Abstractors
|This page contains discussions of experimental/scientific/philosophical/logical aspects of Lojban that are|
non-official and not for everyday usage. You've been warned.
This page is part of a series called Tsani's Interpretations of Controversial Lojban Grammar.
Any abstractors in Lojban are extremely useful with their current definitions, but with The book's definitions not quite matching the way many abstractors are used in current conversations on IRC, I feel the need to explain the way la tsani use these cmavo, in perhaps what is an attempt to make them, overall, more useful.
As for the presence of ce'u within these embedded bridi, I adhere to these rules.
As for subscripting ce'u with xi in the event of a ce'u-type abstraction being contained within an abstraction, I adhere to the rules of relative clauses as outlined in The Book. That is to say that ce'uxire refers to a ce'u of the parent abstraction even if that abstraction is not ce'u-capable, i.e. a member of nu and friends. This is done for the sake of simplicity. Using ce'u without a subscript in a ce'u-incapable clause (nu et al.) is always incorrect, even if that clause is embedded within a ce'u-capable one.
Experimental cmavo proposed in this paper:
- du'au LAhE based on du'u; converts a text into a bridi
- lu'au LAhE based on lu; converts a bridi into a text
- ce'ai ZOhU based on ce'u; denotes a lambda prenex (used to be ce'au)
nu and du'u
These two abstractors constitute the core of this document. Disregarding su'u, it is my belief that all abstractions can be expressed using only nu and du'u (to some degree) and thus that all other abstractors exist only for convenience, or for achieving certain slightly more specific interpretations (as is the case for jei and ni, described near the end of this document).
nu, like its gloss suggests, creates an event, which is bounded in spacetime and has various properties such as its duration and its location(s). It is mainly used after sumtcita, such as and most commonly ca. .i ca lo nu zdani nerkla kei mi co'u cutci dasni -- When I enter my house, I take off my shoes. (For additional explanations on ca and other tenses and sumtcita, see this.)
There are no circumstances for which a nu-clause should contain ce'u; the same goes for nu's friends, li'i, mu'e, pu'u, za'i, and zu'o. Additionally, a nu-clause should never contain an indirect question. That is to say that a nu abstraction must always be "fully applied". See the section on ka for an explanation of "application".
The "return value" of a nu-clause is inherently a fasnu1.
du'u is the predication abstractor, where it differs from nu in that du'u has an x2, namely the text claiming du'u1. Predications are not are not bound in spacetime and have properties such as sumti being related, type of relationship, and modals and connectives involved. A du'u1 is a sort of class of nu1, such that events are instances of predications. That sparked my idea for fasnu2.
There are few brivla that actually use true du'u. In fact, it seems like most of the "facts xN (du'u) about subject xN+1" are actually properties, rather than real predications. For instance, for all uses of djuno where the x3 must find its way into the x2 in order to be semantically correct, djuno2 is a property of djuno3, rather than a du'u. More on that in the section about ka.
du'u's default "return value" is a bridi1, which entails that under my interpretation, bridi1 is a du'u1. A return value that differs from the default is marked using an indirect question: compare lo du'u do klama, lo du'u do klama makau, lo du'u do mokau, and lo du'u mi jikau do klama. There are some questions for which the interpretation is strange: consider lo du'u peikau mi cinba do1, lo du'u fi'akau do cinba fi'akau mi, lo du'u mi sexixokau darxi do, and lodu'u xokaure'u nu mi cinba do. There are two particular indirect questions, namely la'umakau and xukau, that are discussed in the section regarding jei and ni. Of course, as could be seen in the fi'akau example, there's nothing wrong with using multiple indirect questions. As for peikau, it glosses "what you feel about broda" and not "what I feel about broda". (Okay, it could mean "what I feel about broda", but only under a doi mi context, which is silly.)
Some problems arising from Tsani's Interpretations: The Superman/Lois Lane Paradox prompted the creation of two experimental cmavo, which are useful only under very specific circumstances: Tsani's Interpretations: du'au and Tsani's Interpretations: lu'au. Both are members of LAhE and they respectively cast a text into a bridi1 and bridi1 into a text. For example, consider .i ko'a goi lo du'u mi citka ci lo plise. .i mi cusku lu'au ko'a is equivalent in meaning to .i mi cusku lo se du'u mi citka ci lo plise.
ka and si'o
These two abstractors are children of du'u, in the sense that it is possible, using only du'u to express meanings identical to those of ka and si'o. I work under the assumption that a du'u-clause containing at least one ce'u is equivalent to a ka-clause and that a du'u-clause where all sumti places and explicit modal places are ce'u is equivalent to a si'o-clause.
Under my interpretation, ka is hugely useful, in that it supplants many prior uses of nu. In order to properly understand the way that I grasp the property abstraction, it is necessary to understand that Lojban uses a second order logic for this. Consider bebna = x1 is foolish in property x2 and the example mi bebna lo ka ce'u cinba du'ezo'e. Readily, we can see that there is a sort of second-degree predication, namely lo du'u mi cinba du'ezo'e. This is a process that I call application.
Applying a property to a sumti or to sumti means to reduce the property abstraction using ka into a predication abstraction using du'u. To do so, one must determine the referents of the ce'u. For instance, mi mutce lo ka ce'u tavla do makau -> lo du'u mi tavla do makau.
Application is a process handled by the selbri relating the property; the speaker never has to worry about application. In other words, the "property brivla", such as but not limited to kakne, mutce, simxu, zukte, mulno, simsa, and dunli, function in a two-step process of applying the property, and then making a claim about the predication that results from the application.
Note that as a du'u abstraction is called a bridi or proposition, a ka abstraction is called a function, where the ce'u is/are the parameter(s).
Certainly less useful than ka, si'o has a specific function that is difficult or irritating to implement with a du'u abstraction. Under my interpretation, a sidbo1 is not a si'o. I believe that a sidbo1 is simply a property of sidbo2, as understood/created/interpreted by sidbo3.
I understand lo si'o broda as meaning "what is means to broda, for si'o2" or "the meaning of broda, for si'o2" or "<si'o2>'s interpretation of broda".
It turns out that si'o as per this definition greatly resembles latro'a's me'ei, aka the "Article for abstract predicate sumti," save for that si'o allows for more flexibility. For instance, lo si'o citka == me'ei citka assuming that the si'o-abstraction contains no implicit makau, which can be a pain. Now, si'o can certainly contain for more complex selbri than simple me'ei can, because me'ei is a LE, but me'ei has the uncanny ability of being completely unambiguous as to the true nature of its contents: it's definitely a pure selbri.
du'u's friends: ni and jei
ni and jei fall into "du'u's friends" category, rather than the "du'u's children category" which encompasses ka and si'o, due to that there are no required ce'u in a ni/jei-abstraction. However, they remain du'u's friends and not du'u's siblings due to that a simple du'u abstraction can be used to obtain an almost equal meaning. It must be noted that ni and jei do have interpretations slightly different from their du'u-equivalents.
Like a du'u abstraction however, ni and jei abstractions may contain ce'u.
A ni abstraction is vague. It may extract from the bridi either a pure number, a number with units, or a vague sort of comparable-ish thing. In terms of du'u, this is done by means of a sumti indirect question attached to a modal, namely sela'u or la'u, for the first two possible return values, respectively. These modals stem from klani from which ni itself stems.
Considering that properties are not comparable, but that quantities are, a ni abstraction is under my interpretation the correct sumti for the comparison property place of zmadu, mleca, and (on some occasions) dunli.
e.g. mi zmadu do lo ni ce'u certu lo ka ce'u tavla fo lo lojbo "My ability to speak Lojban exceeds yours"
The truth-value abstraction as it's called is in a sense a specialisation of ni, rather than of du'u itself, considering that the return value of jei under my interpretation is a real number in the interval 0, 1. As numbers are comparable, jei abstractions may be used as zmadu/mleca/dunli3, but this is unuseful outside of fuzzy logic contexts. All in all, however, jei has extremely few uses.
In terms of a du'u-approximation, jei is similar to lo du'u xukau broda
The Pre-application of properties
Some places that use du'u in Official Lojban, but ka under my interpretation may be pre-applied, i.e. applied by the speaker and not the selbri. The most notable instance of pre-application is djuno.
Under my interpretation, it would be necessary for all djuno bridi to be of the type ko'a djuno lo ka ce'u brode kei ko'e, which is extremely inconvenient. Thus, for the sake of simplicity, preserving backwards-compatibility as much as possible, and not having to use kei, using a plain, fully-applied du'u is acceptable as a djuno2. If djuno3 is left implicit, it is understood that it is some sumti from the proposition expressed in djuno2.
If djuno2 is fully-applied but djuno3 is specified and is not redundant to any explicit or implicit sumti that are present in the djuno2 proposition, it is defined as being the referent of an implicit ce'u inside the prenex of the djuno2 proposition.
Example of pre-application: mi djuno lo ka ce'u nelci co citka lo plise kei do, mi djuno lo ka do nelci co citka ce'u kei lo plise -> mi djuno lo du'u do nelci co citka lo plise
A list of gismu that I propose should use ka
This list is not exhaustive. Typically, when a selbri has an abstraction place in which another of that bridi's sumti must be in order to achieve understandable semantics, that abstraction place is a property of that sumti. Consider the case of mi kakne lo nu do citka lo plise.
- kakne = x1 is capable of being/doing x2 (ka) under conditions x3 (nu) (It is possible for x2 to be a property of x1 given that x3 occurs/is true)
- zukte = x1 employs means x2 (ka) to bring about/cause x3 (nu) (x3 becoming/remaining true is the intentional antecedent of x2 being a property of x1)
- cirko = x1 loses property x2 (ka) under conditions x3 (nu) (x2 ceases to be a property of x1 given that x3 occurs/is true; no implication of volition; cf. sisti)
- troci = x1 attempts x2 (ka) by actions/method x3 (ka) (x2 becoming/remaining a property of x1 is the result of x3 being a property of x1, setese zukte a'i, no implication of success (x2 might not become a property of x1]
- snada = x1 accomplishes/succeeds at x2 (ka) as a result of attempt x3 (ka) (success version of troci)
- fliba = x1 fails at being/doing x2 (ka) (failure version of troci)
- sisti = x1 ceases to be/do x2 (ka) (x2 being a property of x1 comes to an end as the result of the volition of x1; volitional cirko; snada lo ka cirko)
- zifre = x1 is free to be/do x2 (ka) under conditions x3 (nu) (x1 can acquire or lose property x2, at will, given that x3 occurs/is true)
- bilga = x1 is obliged to be/do x2 (ka) by standard/agreement x3 (nu?) (x2 is a property of x1 disregarding the volition of x1 as a result of x3 occurring/being true)
- fuzme = x1 is responsible/accountable for action x2 (ka) to judge/authority x3 (x3 recognizes that x2 is a property of x1)
- gunka = x1 works/labours at x2 (ka) for purpose/goal/objective x3 (nu) (x3 is the desired antecedent of x2 being a property of x1)
- lazni = x1 is lazy at/avoiding work/effort concerning action x2 (ka)
- tatpi = x1 is tired/fatigued by effort/work/situation x2 (ka)
- surla = x1 is relaxed/relaxing/resting/is at ease at being/doing x2 (ka)
- srera = x1 errs in doing/being x2 (ka), erroneous under conditions x3 (nu) by standard x4 (x4 considers x2 being a property of x1 to be an error, regardless of x1's volition, given that x3 occurs/is true)
- darsi = x1 shows audacity in doing/being x2 (ka)
- virnu = x1 is brave/courageous in doing/being x2 (ka) by standard x3
- bebna = x1 is a fool/idiot/boob at doing/being x2 (ka)
- stati = x1 has a talent/aptitude/innate skill for doing/being x2 (ka)
- tarti = x1 behaves/conducts oneself as/in manner x2 (ka) under conditions x3 (nu) (x2 is volitionally the property of x1 given that x3 occurs/is true; consider "I'm polite around girls" -> mi tarti lo ka clite kei tu'a lo ninmu)
- certu = x1 has skill/shows prowess at doing/being x2 (ka) by standard x3
- sutra = x1 is fast/swift at doing/being x2 (ka)
- masno = x1 is slow/sugglish at doing/being x2 (ka)
- frati = x1 reacts/responds with action x2 (ka) to stimulus x3 (ka) under conditions x4 (nu) (x3 being a property results in x2 being a property of x1 disregarding x1's volition, given that x4 occurs/is true; cf. spuda for a volitional form)
- spuda = x1 answers/replies/responds to x2 (ka) with response x3 (ka) (x3 being a property of x1 is a desired result of x2 being a property of x1; mi spuda lo ka do teryrei lo du'u xukau ce'uxire kanro kei kei fo lo ka ce'u goi ko'a cusku lo sedu'u ko'a ja'a kanro "The answer that I tell you when you ask me how healthy I am is that I'm indeed healthy." As that's extremely wordy, sumti raising becomes a very viable option: mi spuda tu'a lo du'u xukau kanro kei tu'a lo sedu'u ja'a kanro)
- bredi = x1 is ready/prepared for x2 (ka)
- rivbi = x1 avoids/shuns/escapes/skirts fate x2 (nu) by action/state x3 (ka) (x2 is not true/doesn't occur as a result of x3 being a property of x1, as per x1's volition)
- zajba = x1 is a gymnast at/performs gymnastics feat x2 (ka)
- Tsani's Interpretations: The case against cinse = x1, in activity/state x2 (ka), exhibits sexuality/gender/sexual orientation x3 (ka) by standard x4
- kamni = x1 (mass) is a committee with task/purpose x2 (ka) of body x3
- vecnu (the gimste agrees with me here) = x1 sells x2 (ka) to x3 for price x4 (a money transaction between x1 and x3 (x3 giving money to x1) results in x3 acquiring property x2)
Difference between kakne and zifre: compare mi kakne lo ka ce'u co'a morsi kei lo ka ce'u goi ko'a pinxe lo vindu be ko'a and mi zifre lo ka ce'u co'a morsi kei lo ka ce'u goi ko'a pinxe lo vindu be ko'a. Where kakne says nothing about volition, zifre indicates that as a result of the combined truth of zifre3 and zifre1's desire to zifre2, zifre2 can be a property of zifre1. I extend the meaning of zifre to include acquiring and losing the property, at will, so long as zifre3 is in effect.
Problems with using ka; "How do I say X?"
Some of you might complain that using these properties instead of events for some gismu, such as bredi, makes them less useful, but I argue that a form of sumti raising answers that problem. How to say, under my interpretation, "I'm ready for the end of the world" ? Under official Lojban, let's say that mi bredi lo nu fanmo pe'a lo munje glosses the English sentence. Then, ask yourself, "What is that that I'm ready for?" You can't be prepared for an event; you can however be prepared to experience that event. Thus, I consider mi bredi lo ka ce'u lifri lo nu fanmo pe'a lo munje, which is long, but which can be reduced into mi bredi tu'a lo nu fanmo pe'a lo munje (yes, it's one of those "I'm raising an event O_o" situations) or into mi seli'i fanmo pe'a lo munje kei bredi or into the more afterthought form involving co, mi bredi co seli'i fanmo pe'a lo munje, as being a better solution.
Another notable ka-ification is that of sisti, which I differentiate from cirko with volition. That is to say that lo si'o sisti cu si'o zukte lo ka ce'u cirko ce'uxire. In order to get at the "old" version of sisti, I'd use zukte fi lo nu xy tolcfa.
mi tatpi lo nu do krixa doesn't make any sense, clearly. Y screaming is not a situation that tires X, but X experiencing Y screaming is. This is another example of a broda lo kaseli'i brode.
co becomes a real jewel as it lets us avoid a lot of description and abstraction boilerplate. Consider the previous example, zukte fi lo nu tolcfa. We can readily reduce this into zukte co tolcfa (this necessarily resolves into tolcfa as zukte3 because a cfari1 is an event and not a property and therefore would be semantically uninterpretable as a zukte2). Similarly, kakne lo ka broda can be transformed into kakne co broda. This was possible before this ka-revolution, and is thus not an antecedent of my proposal, but I do advocate furthering the use of co in order to reduce the number of uses of lo and various abstraction markers.
For example, consider that mi ce do simxu lo ka ce'u kansa ce'u lo ka ce'u zgana lo nu lo pendo be vo'a cu dansu je tigni can be reduced into mi ce do simxu co kansa co zgana co seke dansu tigni lo vo'a pendo, a seven word and ten syllable gain, reducing in this case by almost 30% the length of the sentence.
Yes, this system involves more words for a lot of constructs, (if you're a co-hater, that is,) but now we have a more consistent type system that lets us pass around properties like so: mi bredi lo na se kakne be do, do djuno lo mi se zifre.
A Lambda prenex
Initially, ce'u was meant to be a PA, lambda-quantifying an otherwise logically-quantified variable (the da-series). Perhaps it is worth reviving this idea, although slightly modified, in an attempt to fix nested abstractions, which are otherwise messy, what with all the required subscripting. The original idea was for ka abstractions to be of the form lo ka ce'u da broda da (remember, ce'u in there is a PA) for a reflexive property, and lo ka ce'u da broda ce'u de for non-reflexive properties.
Let ce'ai be a member of ZOhU, denoting a lambda prenex, where all variables are understood to be lambda-quantified:
- lo ka da ce'ai da prami da the property of loving oneself.
- lo ka da de ce'ai da broda lo ka di ce'ai de brode di In here, de is referring a ce'uxire.
In this system, we can mix ce'ai prenexes with regular ce'u without fear. ce'u is thus treated as the afterthought form.
Using a ce'ai prenex more closely parallels lambda calculus from which the description of properties is largely based in this document.
It is also possible to mix logically prenexes with lambda prenexes, as even in official Lojban, multiple ZOhU-clauses are permitted:
lo ka da zo'u de ce'ai de se prami da is "being loved by something/someone".
Some notable formulae
Note: dy. ubu is my pet name for the identity property, such that:
.i ca'e dy. ubu ka ce'u du makau
Under this interpretation of abstractors, the following is true:
- ko'a ckaji lo ka ce'u broda = ko'a broda
- ko'a dunli ko'e lo ka ce'u broda = ko'a .o ko'e broda
- ko'a zmadu ko'e lo ka ce'u broda = ko'a .enai ko'e broda
- ko'a zmadu ko'e lo ni ce'u broda = lo ni ko'a broda cu zmadu lo ni ko'e broda kei dy. ubu
- ko'a co'a ckaji lo ka ce'u broda = ko'a binxo lo ka ce'u broda
- ko'a co'u ckaji lo ka ce'u broda = ko'a cirko lo ka ce'u broda
- ko'a sisti lo ka ce'u broda = ko'a zukte lo ka ce'u cirko lo ka ce'u broda
- lo si'o binxo cu si'o tolcri .i je lo si'o cirko cu si'o tolbi'o
And others that I haven't either the time to define or yet determined.